Monte-Carlo Simulation of SC2 Ladder

Witness the lengths forum trolls must go through to protect themselves from admitting someone else might have a point about the balance of SC2. A race being underpowered creates under-representation in both upper and lower leagues, with representation peaking in middle leagues. That’s a fact. Sorry it makes you so mad.

Witness the lengths forum trolls must go through to protect themselves from admitting someone else might have a point about SC2.

An "Internet troll " or " Forum Troll " is a person who posts messages to bait people to answer. Trolls often delight in sowing discord on the forums . A troll is someone who inspires flaming rhetoric, someone who is purposely provoking and pulling people into flaming discussion.

Don’t take it that I’m calling you any sort of special troll, as you can see you fit the definition of a plain old boring troll.

Ya. I should’ve given up a long time ago. Especially after I realized he didn’t even understand what my argument was, and claimed I’d said things I didn’t. Impossible to reason with someone on complicated topics when they can’t even understand you on the simple ones :man_shrugging:

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Funny because I created the topic to share some results I found, which I thought were interesting facts about SC2. Forum trolls go into threads and try to derail them with off topic and generally inflammatory messages (guess what you are doing).

Kid you aren’t even using the right terminology. After you can use the correct words THEN you have taken the very first step towards being able to play the authority card, NOT before.

You called this “predictive analytics” but that’s literally the opposite of what is going on. We aren’t predicting the future, we are analyzing the past which is called descriptive analytics.

Not only that but you repeatedly assert you are correct while refusing to provide any proof for any of your points, while saying I am wrong despite having provided proof.

This isn’t a sound argument. This is borderline delusion.

I’m… a bit concerned… that anyone would try this hard to convince us that Zerg really does have it the worst.

My only response is “play more Terran”.

Congrats, I used one wrong word.

You misunderstood an entire conversation.

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It’s a fun mathematical exercise, and by the comments you can tell these forum trolls direly need it.

I understand it better than you do. You said an answer being correct isn’t proof that the algorithm that produced the answer is correct. We talked about the theory but it went far over your head. You said you could write a wrong algorithm to get the right answer and since you were struggling with the theory I decided to bring it back into the real world. I asked you to back your claim up with evidence, aka to create a wrong algorithm that gives the correct answer. You refused, thus proving my point.

Sure, it might be fun, but dude, Zerg doesn’t have it “bad” by any stretch of the imagination, no matter what your colorful charts and “simulations” may think they are telling ya.

:crazy_face:

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So, being 22% in GM while Protoss is 45% in GM means Zerg doesn’t have it bad? GM has literally never been more imbalanced than it is currently. If you reject the concept of imbalance during the most imbalanced period in SC2, you’ve rejected the concept of imbalance, period, and that is absurd.

It’s a fact that zerg is underpowered. This post simply shows that the distribution of the races on the rest of the ladder meshes well with that fact.

You can choose any historical point as a starting point. It should be obvious but since you seem to struggle I helped you with some meaningful possible dates.

Which would be useful if we knew what those percentages were and where you arbitrarily decided each league to stop (not to mention, again, what’s the percentage of professionals and GMs according to you).

I am trying to explain to you that your graphs are completely useless and what needs to be done so they can be usable. I mentioned research papers to be nice and because those kinds of mistakes can happen even there but truth be told even a 6th grade doing graphs for the first time is told to put scales and a title.

I wrongly tried to be nice, mea culpa. I am holding you to the standard of a 6th grader for the next graphs you do, please don’t disappoint me again.

Not quite that hard since I can choose the hypothesis and therefore choose to use any curve I like as the “temperature curve” and then can use any funky correlation I like. The one challenging thing, I’ll grant you that, is that terrans and zergs curves have an opposite behavior with toss in between and that makes my graph (hot stuff terrans, cool kids toss, OP bugs) harder to make than the graph (cool kids terrans, hellfire OP bugs and laser aliens).

That was a beautiful sentence even for you.
You do assume it (wrongly, you also assume other people agree with you on that (wrongly) and you somehow believe an unrelated sentence of me meant I agree with you. Bonus point you misused, again, the Pareto principle.

I answered to your wrong distribution in the other thread but I’ll address the comment about the population which tripled … it did. Where are these new players? Are they more concentrated in the lower leagues (causing the ones who did not stop to rank up)? Do they play less or more? Many interesting questions you have no clue about. The assumptions you made were once again just complete misunderstanding of what is being said and getting to random unrelated conclusions you feel (wrongly) to be true possibly because of other completely unrelated events you also misinterpreted.

And again, no Newton was not thinking about you when he proved gravity existed and gravity does not prove (or disprove for that matter) the many odds ideas you have.

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If you were to, then you’d pretty much be doubling the number of assumptions that you make, which, again, is contrary to the goal.

I stated very specifically in the OP that everything was tuned to match the real world as closely as possible. This includes league percentiles. Reading is your friend!

That might be true if you were providing constructive feedback, rather than making your own assumptions and then blaming me for them. Half the things you say confirm what I am saying but you say I am wrong which means you either don’t understand what you are saying or you don’t understand what I am saying.

Please do. I await your exact algorithm and inputs.

No I don’t, I verified it empirically and showed that in a simulation it produces the same result. In the other thread, you accidentally let it slip that I was right on this point.

Again, this is another instance where the behavior of the algorithm models the SC2 ladder as closely as possible. Players start out in the middle leagues. It assumes they are roughly average.

I don’t alter them, I write them exactly as you say them(left to right). if there is a problem is in your explanation or smarter people then you selected distribution inside the natural numbers(_https://www.quora.com/Can-Elo-ratings-be-negative) because it’s easier to read, understand and calculate.

_The Mathematics of Elo Ratings. Calculating the relative skill of… | by Jørgen Veisdal | Cantor’s Paradise

As per the information in section performance mean it’s not arbitrary:
“…Elo’s key assumption is that the performance of each player in each game is a random variable which over time conforms to a Bell curve-shaped probability distribution. In other words, in Elo ratings systems, a player’s true skill is represented by the the mean of that player’s random performance variable…”

In simple terms, true skill is a number inside Bell curve-shaped probability distribution that is created from collecting random variables into data set.

Link above.

Punching the wrong variables into the wrong places in the equation is not my fault. The fact that I listed them in a particular order does not change their order inside the actual equation.

If a player has X more elo than his opponent, his win-rate vs that opponent will be the same no matter if his elo is 900 or 90000 or 208213123219. When you compute 800 vs 700 the first player will have 100 more elo. You are computing -800 vs -700, meaning player A has -100 elo. You’ve altered which player has the 100 elo advantage - in one calculation it’s player A and in the next it’s player B.

That link confirms what I’ve been saying. You can pick any value for the mean. It’s arbitrary.

You are conflating the mean of the player’s performance with the mean of the distribution, which are two totally different things.

Yet another prediction of my theory has been verified empirically. If the rankings of the middle leagues are controlled by new players, who haven’t played many games, and if Zergs are being demoted from higher leagues due to balance, then:

  1. The middle leagues should have many players with very few games played (confirmed).
  2. There should be a correlation between games played and negative rank (confirmed).
  3. There should be a higher number of games played for Zergs than for Protoss (confirmed) since higher-ranked Zergs are being demoted into the region populated by mostly new players.

Best-fit estimation of SC2 ladder data finds almost identical results to the SC2 pro scene. Batz’s models win yet again.

Seems like a good time to bring back this post